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Search: id:A094793
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| 9, 53, 181, 465, 1001, 1909, 3333, 5441, 8425, 12501, 17909, 24913, 33801, 44885, 58501, 75009, 94793, 118261, 145845, 178001, 215209, 257973, 306821, 362305, 425001, 495509, 574453, 662481, 760265, 868501, 987909, 1119233, 1263241
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OFFSET
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0,1
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COMMENT
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Number of injections from {1,2,3,4} to {1,2,...,n} with no fixed points. - Fiona T. Brunk (fbrunk(AT)mcs.st-and.ac.uk), May 23 2006
In general (cf. A094792, A094794, A094795, etc.), the number of injections [k] -> [n] with no fixed points is given by sum((-1)^i*binomial(k,i)*(n-i)!/(n-k)!,i=0..k), which is equal to (1/n!)*f_k(n) where f_k(n) gives the k-th differences of factorial numbers. - Fiona T. Brunk (fbrunk(AT)mcs.st-and.ac.uk), May 23 2006
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FORMULA
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a(n)=n^4 + 6*n^3 + 17*n^2 + 20*n + 9
a(n) = sum((-1)^i*binomial(4,i)*(n-i)!/(n-4)!,i=0..4) - Fiona T. Brunk (fbrunk(AT)mcs.st-and.ac.uk), May 23 2006
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CROSSREFS
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Cf. A001563, A001564, A001565, A001688, A001689, A023043.
Sequence in context: A163941 A159598 A156544 this_sequence A036425 A126085 A055854
Adjacent sequences: A094790 A094791 A094792 this_sequence A094794 A094795 A094796
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 11 2004
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